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Handbook of Computer Aided Geometric Design by M.-S. Kim, J. Hoschek, G. Farin

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Chapter 17

Pythagorean-Hodograph Curves

Rida T. Farouki

17.1 PREAMBLE

With the advent of a new millenium, it seems appropriate to begin with a brief historical perspective on a topic that entails a remarkable confluence of ideas spanning nearly 4000 years of geometry and algebra. Figure 17.1shows cuneiform tablet No. 322 in the Plimpton Collection of the Rare Book & Manuscript Library, Columbia University. This compilation of sexagecimal numbers, composed in the Old Babylonian Period (˜ 1900 to 1600 BC), was discovered in the 1920s and subsequently deciphered by Neugebauer and Sachs [54] in 1945. Far from being a mere financial or commercial record, the tablet reveals profound knowledge [8] of the fundamental characterization

Figure 17.1 ...

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